In Chihuahua, the capital of the northern Chihuahua state, at least 30 armed men stormed the second floor of Christian Faith and Life Temple, a drug rehabilitation centre, killing 19 people and wounding four others.
Police said the rehabilitation clinic may have housed members of the Los Mexicles gang linked to the Sinaloa cartel, which is warring with Los Aztecos, affiliated with the Juarez cartel.
In the other attack, an unknown number of assailants carried out a series of armed raids and executions across the town of Madero, in the northeastern state of Tamaulipas, police said.
The attacks reportedly began on Thursday, with confrontations between police and a group of armed men moving around the city in vans.
Authorities then received reports on Friday that bodies had been discovered on a local beach and in other locations throughout the town.
So far, "20 bodies have been found in different parts of the city", a federal police officer said.
In September 2009, two similar attacks in nearby Ciudad Juarez left a total of 28 dead.
Some 23,000 people have died in soaring drug-related violence following the launch of a military clampdown on organised crime, involving some 50,000 troops, at the end of 2006.
Illegal drug trade
The profitable trade in illegal drugs has allowed cartels to arm themselves with the latest and most deadly weapons available.
Those weapons often come from the United States, and Calderon last month urged US lawmakers to strengthen gun laws, warning that over 90 per cent of the guns used by drug traffickers in Mexico come from north of the border.
"Believe me, many of these guns are not going to honest American hands. Instead thousands are ending up in the hands of criminals," he said.
Calderon has scored some victories, including the arrest of top cartel leader Jose Antonio Medina, dubbed the "King of Heroin" and the death of Arturo Beltran Leyva, known as the "chief of chiefs."
But he also faces growing resentment from residents in the worst-affected parts of Mexico, who are angry at his failure to stop the violence and accuse the troops he has deployed of committing abuses.